Linear time single-source shortest path algorithms in Euclidean graph classes
Computational Geometry
2026-03-25 v1
Abstract
In the celebrated paper of Henzinger, Klein, Rao and Subramanian (1997), it was shown that planar graphs admit a linear time single-source shortest path algorithm. Their algorithm unfortunately does not extend to Euclidean graph classes. We give criteria and prove that any Euclidean graph class satisfying the criteria admits a linear time single-source shortest path algorithm. As a main ingredient, we show that the contracted graphs of these Euclidean graph classes admit sublinear separators.
Cite
@article{arxiv.2603.22948,
title = {Linear time single-source shortest path algorithms in Euclidean graph classes},
author = {Joachim Gudmundsson and Yuan Sha and Sampson Wong},
journal= {arXiv preprint arXiv:2603.22948},
year = {2026}
}